On fixed edges and edge-reconstruction of series-parallel networks

Abstract

An edge e of a graph G is said to be a fixed edge if G - e + e′ ≅ G implies that e′ = e, and a forced edge if G - e + e′ is an edge-reconstruction of G implies that e′ = e. In this paper, we use the method of excludable configurations to investigate the fixed edges and the forced edges of series-parallel networks. It is proved that all series-parallel networks contain fixed edges except P3 V K1 and P4 V K1, and that all series-parallel networks are edge-reconstructible. © Springer-Verlag 2001.